(I don't know if these have a proper name, and I'd be rather surprised if they don't, but...)

The Benjamin's Blog's mathematicians at Benjamin's Blog headquarters had spent so much time doing Sudoku, Kakuros, and analysing election results in Harrow-on-the-Hill that one day they decided to get their revenge. They locked to the door, grabbed some shapes, lines, and numbers, and performed some ghastly experiments on them, until, suddenly, one day, they had at last created something with which they could frustrate the world, and, just to make things worse, they gave it the most ridiculous name in the world: the Kjarposko.

It involves a selection of boxes which are linked together. Each box is divided into two sections - there is a number on top and a space underneath.

There's only two rules: every number on top of a box equals the total of the answers in the bottom of the box linked to it and no number may be used more than once. (A list of numbers you may use will be provided).

Confused? Don't panic. Let me guide you through an example.

You need to put 1, 2, and 3 into the three boxes. The box with 4 in it is linked to the boxes with the 3 on top and the 5 on top. Therefore, the numbers you put into the '3' and '5' box must add up to 4. In the same way '3' + '4' = 5 and '4' + '5' = 3.

Righty-ho, then:

I suggest fitting a smoke detector to your head to attempt these.

BRAIN TEMPERATURE: NORMAL

BRAIN TEMPERATURE: HOT

BRAIN TEMPERATURE: SIZZLING

BRAIN TEMPERATURE: CRITICAL

BRAIN TEMPERATURE: TOO HOT FOR WORDS

WARNING

You are now approaching one of the most lethal puzzles on the planet. It is so hard that it is on the edge of meltdown and some of the numbers have evaporated into * symbols. It is still possible to fill in the answers, but if you are of a nervous disposition DO NOT ATTEMPT THIS PUZZLE.

The book you got these from, is it the Gideon Osbourne book of mathematics?

No, the book uses letters in the example, but I thought that would be far too complicated to understand. Hence I used '3' rather than 3 to indicate that it's not the number 3, like putting ' in front of a number in Excel.

To make the "5" box correct, the highest number that can go in the "20" box is 4, but that immediately makes the middle "22" box impossible. Am I missing something? (Or are there connecting lines missing, or maybe the numbers are wrong?)

Royal Oak to Bethnal Green in 333 days
Heathrow Terminal 4 to Amersham in 17 hours, 42 minutes and 22 seconds